Calculate the root mean square velocity of nitrogen molecules at 25°C.
A) 729 m/s
B) 515 m/s
C) 149 m/s
D) 297 m/s

Question

Quizplus · Accepted Answer

The root mean square velocity ($v_{rms}$) of a gas can be calculated using the formula $v_{rms} = \sqrt{\frac{3kT}{m}}$, where $k$ is the Boltzmann constant ($1.38 \times 10^{-23} J/K$), $T$ is the temperature in Kelvin, and $m$ is the mass of a single molecule in kilograms. For nitrogen ($N_2$), the molar mass is 28.02 g/mol, which is $28.02 \times 10^{-3} kg/mol$. Since there are $6.022 \times 10^{23}$ molecules in a mole (Avogadro's number), the mass of a single nitrogen molecule is $\frac{28.02 \times 10^{-3}}{6.022 \times 10^{23}} kg$. The temperature in Kelvin is $25°C + 273.15 = 298.15 K$. Substituting these values into the formula gives a $v_{rms}$ close to 515 m/s.

Calculate the Root Mean Square Velocity of Nitrogen Molecules at 25°C